Training a Yes/No NN for Image Classes
Yes, you can train a NN to detect only one type of object like a table. However, you probably will not want to train such a NN from scratch by showing some examples of tables and non-tables. You will need to use transfer learning on a model already trained on several image classes and teach it to also recognize your new class. This transfer learning requires a smaller set of desired images. You may need to give it some negative examples also. You should explore transfer learning with mobilenet, inception, and other pre-trained Tensorflow models if you are willing to use Python and Tensorflow